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-rw-r--r--src/math/atan2.c68
-rw-r--r--src/math/atan2f.c59
-rw-r--r--src/math/atan2l.c36
-rw-r--r--src/math/atanl.c13
4 files changed, 73 insertions, 103 deletions
diff --git a/src/math/atan2.c b/src/math/atan2.c
index 825a38fe..5a1903c6 100644
--- a/src/math/atan2.c
+++ b/src/math/atan2.c
@@ -39,75 +39,63 @@
#include "libm.h"
-// FIXME
-static const volatile double
-tiny = 1.0e-300;
static const double
-pi_o_4 = 7.8539816339744827900E-01, /* 0x3FE921FB, 0x54442D18 */
-pi_o_2 = 1.5707963267948965580E+00, /* 0x3FF921FB, 0x54442D18 */
-pi = 3.1415926535897931160E+00; /* 0x400921FB, 0x54442D18 */
-static const volatile double
+pi = 3.1415926535897931160E+00, /* 0x400921FB, 0x54442D18 */
pi_lo = 1.2246467991473531772E-16; /* 0x3CA1A626, 0x33145C07 */
double atan2(double y, double x)
{
double z;
- int32_t k,m,hx,hy,ix,iy;
- uint32_t lx,ly;
+ uint32_t m,lx,ly,ix,iy;
- EXTRACT_WORDS(hx, lx, x);
- ix = hx & 0x7fffffff;
- EXTRACT_WORDS(hy, ly, y);
- iy = hy & 0x7fffffff;
- if ((ix|((lx|-lx)>>31)) > 0x7ff00000 ||
- (iy|((ly|-ly)>>31)) > 0x7ff00000) /* x or y is NaN */
+ if (isnan(x) || isnan(y))
return x+y;
- if ((hx-0x3ff00000 | lx) == 0) /* x = 1.0 */
+ EXTRACT_WORDS(ix, lx, x);
+ EXTRACT_WORDS(iy, ly, y);
+ if ((ix-0x3ff00000 | lx) == 0) /* x = 1.0 */
return atan(y);
- m = ((hy>>31)&1) | ((hx>>30)&2); /* 2*sign(x)+sign(y) */
+ m = ((iy>>31)&1) | ((ix>>30)&2); /* 2*sign(x)+sign(y) */
+ ix = ix & 0x7fffffff;
+ iy = iy & 0x7fffffff;
/* when y = 0 */
if ((iy|ly) == 0) {
switch(m) {
case 0:
- case 1: return y; /* atan(+-0,+anything)=+-0 */
- case 2: return pi+tiny; /* atan(+0,-anything) = pi */
- case 3: return -pi-tiny; /* atan(-0,-anything) =-pi */
+ case 1: return y; /* atan(+-0,+anything)=+-0 */
+ case 2: return pi; /* atan(+0,-anything) = pi */
+ case 3: return -pi; /* atan(-0,-anything) =-pi */
}
}
/* when x = 0 */
if ((ix|lx) == 0)
- return hy < 0 ? -pi_o_2-tiny : pi_o_2+tiny;
+ return m&1 ? -pi/2 : pi/2;
/* when x is INF */
if (ix == 0x7ff00000) {
if (iy == 0x7ff00000) {
switch(m) {
- case 0: return pi_o_4+tiny; /* atan(+INF,+INF) */
- case 1: return -pi_o_4-tiny; /* atan(-INF,+INF) */
- case 2: return 3.0*pi_o_4+tiny; /* atan(+INF,-INF) */
- case 3: return -3.0*pi_o_4-tiny; /* atan(-INF,-INF) */
+ case 0: return pi/4; /* atan(+INF,+INF) */
+ case 1: return -pi/4; /* atan(-INF,+INF) */
+ case 2: return 3*pi/4; /* atan(+INF,-INF) */
+ case 3: return -3*pi/4; /* atan(-INF,-INF) */
}
} else {
switch(m) {
- case 0: return 0.0; /* atan(+...,+INF) */
- case 1: return -0.0; /* atan(-...,+INF) */
- case 2: return pi+tiny; /* atan(+...,-INF) */
- case 3: return -pi-tiny; /* atan(-...,-INF) */
+ case 0: return 0.0; /* atan(+...,+INF) */
+ case 1: return -0.0; /* atan(-...,+INF) */
+ case 2: return pi; /* atan(+...,-INF) */
+ case 3: return -pi; /* atan(-...,-INF) */
}
}
}
- /* when y is INF */
- if (iy == 0x7ff00000)
- return hy < 0 ? -pi_o_2-tiny : pi_o_2+tiny;
+ /* |y/x| > 0x1p64 */
+ if (ix+(64<<20) < iy || iy == 0x7ff00000)
+ return m&1 ? -pi/2 : pi/2;
- /* compute y/x */
- k = (iy-ix)>>20;
- if (k > 60) { /* |y/x| > 2**60 */
- z = pi_o_2+0.5*pi_lo;
- m &= 1;
- } else if (hx < 0 && k < -60) /* 0 > |y|/x > -2**-60 */
- z = 0.0;
- else /* safe to do y/x */
+ /* z = atan(|y/x|) without spurious underflow */
+ if ((m&2) && iy+(64<<20) < ix) /* |y/x| < 0x1p-64, x<0 */
+ z = 0;
+ else
z = atan(fabs(y/x));
switch (m) {
case 0: return z; /* atan(+,+) */
diff --git a/src/math/atan2f.c b/src/math/atan2f.c
index 96839cba..c634d00f 100644
--- a/src/math/atan2f.c
+++ b/src/math/atan2f.c
@@ -15,72 +15,63 @@
#include "libm.h"
-static const volatile float
-tiny = 1.0e-30;
static const float
-pi_o_4 = 7.8539818525e-01, /* 0x3f490fdb */
-pi_o_2 = 1.5707963705e+00, /* 0x3fc90fdb */
-pi = 3.1415927410e+00; /* 0x40490fdb */
-static const volatile float
+pi = 3.1415927410e+00, /* 0x40490fdb */
pi_lo = -8.7422776573e-08; /* 0xb3bbbd2e */
float atan2f(float y, float x)
{
float z;
- int32_t k,m,hx,hy,ix,iy;
+ uint32_t m,ix,iy;
- GET_FLOAT_WORD(hx, x);
- ix = hx & 0x7fffffff;
- GET_FLOAT_WORD(hy, y);
- iy = hy & 0x7fffffff;
- if (ix > 0x7f800000 || iy > 0x7f800000) /* x or y is NaN */
+ if (isnan(x) || isnan(y))
return x+y;
- if (hx == 0x3f800000) /* x=1.0 */
+ GET_FLOAT_WORD(ix, x);
+ GET_FLOAT_WORD(iy, y);
+ if (ix == 0x3f800000) /* x=1.0 */
return atanf(y);
- m = ((hy>>31)&1) | ((hx>>30)&2); /* 2*sign(x)+sign(y) */
+ m = ((iy>>31)&1) | ((ix>>30)&2); /* 2*sign(x)+sign(y) */
+ ix &= 0x7fffffff;
+ iy &= 0x7fffffff;
/* when y = 0 */
if (iy == 0) {
switch (m) {
case 0:
- case 1: return y; /* atan(+-0,+anything)=+-0 */
- case 2: return pi+tiny; /* atan(+0,-anything) = pi */
- case 3: return -pi-tiny; /* atan(-0,-anything) =-pi */
+ case 1: return y; /* atan(+-0,+anything)=+-0 */
+ case 2: return pi; /* atan(+0,-anything) = pi */
+ case 3: return -pi; /* atan(-0,-anything) =-pi */
}
}
/* when x = 0 */
if (ix == 0)
- return hy < 0 ? -pi_o_2-tiny : pi_o_2+tiny;
+ return m&1 ? -pi/2 : pi/2;
/* when x is INF */
if (ix == 0x7f800000) {
if (iy == 0x7f800000) {
switch (m) {
- case 0: return pi_o_4+tiny; /* atan(+INF,+INF) */
- case 1: return -pi_o_4-tiny; /* atan(-INF,+INF) */
- case 2: return 3.0f*pi_o_4+tiny; /*atan(+INF,-INF)*/
- case 3: return -3.0f*pi_o_4-tiny; /*atan(-INF,-INF)*/
+ case 0: return pi/4; /* atan(+INF,+INF) */
+ case 1: return -pi/4; /* atan(-INF,+INF) */
+ case 2: return 3*pi/4; /*atan(+INF,-INF)*/
+ case 3: return -3*pi/4; /*atan(-INF,-INF)*/
}
} else {
switch (m) {
case 0: return 0.0f; /* atan(+...,+INF) */
case 1: return -0.0f; /* atan(-...,+INF) */
- case 2: return pi+tiny; /* atan(+...,-INF) */
- case 3: return -pi-tiny; /* atan(-...,-INF) */
+ case 2: return pi; /* atan(+...,-INF) */
+ case 3: return -pi; /* atan(-...,-INF) */
}
}
}
- /* when y is INF */
- if (iy == 0x7f800000)
- return hy < 0 ? -pi_o_2-tiny : pi_o_2+tiny;
+ /* |y/x| > 0x1p26 */
+ if (ix+(26<<23) < iy || iy == 0x7f800000)
+ return m&1 ? -pi/2 : pi/2;
- /* compute y/x */
- k = (iy-ix)>>23;
- if (k > 26) { /* |y/x| > 2**26 */
- z = pi_o_2 + 0.5f*pi_lo;
- m &= 1;
- } else if (k < -26 && hx < 0) /* 0 > |y|/x > -2**-26 */
+ /* z = atan(|y/x|) with correct underflow */
+ if ((m&2) && iy+(26<<23) < ix) /*|y/x| < 0x1p-26, x < 0 */
z = 0.0;
- else /* safe to do y/x */
+ else
z = atanf(fabsf(y/x));
switch (m) {
case 0: return z; /* atan(+,+) */
diff --git a/src/math/atan2l.c b/src/math/atan2l.c
index 7cb42c2f..e0167d09 100644
--- a/src/math/atan2l.c
+++ b/src/math/atan2l.c
@@ -29,26 +29,22 @@ long double atan2l(long double y, long double x)
{
union IEEEl2bits ux, uy;
long double z;
- int32_t k,m;
- int16_t exptx, expsignx, expty, expsigny;
+ int m;
+ uint16_t exptx, expsignx, expty, expsigny;
+ if (isnan(x) || isnan(y))
+ return x+y;
+ if (x == 1)
+ return atanl(y);
uy.e = y;
expsigny = uy.xbits.expsign;
expty = expsigny & 0x7fff;
ux.e = x;
expsignx = ux.xbits.expsign;
exptx = expsignx & 0x7fff;
- if ((exptx==0x7fff &&
- ((ux.bits.manh&~LDBL_NBIT)|ux.bits.manl)!=0) || /* x is NaN */
- (expty==0x7fff &&
- ((uy.bits.manh&~LDBL_NBIT)|uy.bits.manl)!=0)) /* y is NaN */
- return x+y;
- if (expsignx==0x3fff && ((ux.bits.manh&~LDBL_NBIT)|ux.bits.manl)==0) /* x=1.0 */
- return atanl(y);
m = ((expsigny>>15)&1) | ((expsignx>>14)&2); /* 2*sign(x)+sign(y) */
- /* when y = 0 */
- if (expty==0 && ((uy.bits.manh&~LDBL_NBIT)|uy.bits.manl)==0) {
+ if (y == 0) {
switch(m) {
case 0:
case 1: return y; /* atan(+-0,+anything)=+-0 */
@@ -56,9 +52,8 @@ long double atan2l(long double y, long double x)
case 3: return -2*pio2_hi-0x1p-120f; /* atan(-0,-anything) =-pi */
}
}
- /* when x = 0 */
- if (exptx==0 && ((ux.bits.manh&~LDBL_NBIT)|ux.bits.manl)==0)
- return expsigny < 0 ? -pio2_hi-0x1p-120f : pio2_hi+0x1p-120f;
+ if (x == 0)
+ return m&1 ? -pio2_hi-0x1p-120f : pio2_hi+0x1p-120f;
/* when x is INF */
if (exptx == 0x7fff) {
if (expty == 0x7fff) {
@@ -78,17 +73,12 @@ long double atan2l(long double y, long double x)
}
}
/* when y is INF */
- if (expty == 0x7fff)
- return expsigny < 0 ? -pio2_hi-0x1p-120f : pio2_hi+0x1p-120f;
+ if (exptx+120 < expty || expty == 0x7fff)
+ return m&1 ? -pio2_hi-0x1p-120f : pio2_hi+0x1p-120f;
- /* compute y/x */
- k = expty-exptx;
- if(k > LDBL_MANT_DIG+2) { /* |y/x| huge */
- z = pio2_hi+0x1p-120f;
- m &= 1;
- } else if (expsignx < 0 && k < -LDBL_MANT_DIG-2) /* |y/x| tiny, x<0 */
+ if ((m&2) && expty+120 < exptx) /* |y/x| tiny, x<0 */
z = 0.0;
- else /* safe to do y/x */
+ else
z = atanl(fabsl(y/x));
switch (m) {
case 0: return z; /* atan(+,+) */
diff --git a/src/math/atanl.c b/src/math/atanl.c
index e76693e4..d29e6316 100644
--- a/src/math/atanl.c
+++ b/src/math/atanl.c
@@ -70,8 +70,8 @@ long double atanl(long double x)
union IEEEl2bits u;
long double w,s1,s2,z;
int id;
- int16_t expsign, expt;
- int32_t expman;
+ uint16_t expsign, expt;
+ uint32_t expman;
u.e = x;
expsign = u.xbits.expsign;
@@ -81,15 +81,16 @@ long double atanl(long double x)
((u.bits.manh&~LDBL_NBIT)|u.bits.manl)!=0) /* NaN */
return x+x;
z = atanhi[3] + 0x1p-120f;
- return expsign < 0 ? -z : z;
+ return expsign>>15 ? -z : z;
}
/* Extract the exponent and the first few bits of the mantissa. */
/* XXX There should be a more convenient way to do this. */
expman = (expt << 8) | ((u.bits.manh >> (LDBL_MANH_SIZE - 9)) & 0xff);
if (expman < ((0x3fff - 2) << 8) + 0xc0) { /* |x| < 0.4375 */
if (expt < 0x3fff - 32) { /* if |x| is small, atanl(x)~=x */
- /* raise inexact if x!=0 */
- FORCE_EVAL(x + 0x1p120f);
+ /* raise underflow if subnormal */
+ if (expt == 0)
+ FORCE_EVAL((float)x);
return x;
}
id = -1;
@@ -122,6 +123,6 @@ long double atanl(long double x)
if (id < 0)
return x - x*(s1+s2);
z = atanhi[id] - ((x*(s1+s2) - atanlo[id]) - x);
- return expsign < 0 ? -z : z;
+ return expsign>>15 ? -z : z;
}
#endif
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